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Everything about Ultrafilter
Maximal proper filter
In the mathematical field of order theory, an ultrafilter on a given partially ordered set is a certain subset of namely a maximal filter on that is, a proper filter on that cannot be enlarged to a bigger proper filter on Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: UltrafilterA 5-minute orientation
- Skim a recent paper: Choice of Ultrafilter Affects Recovery Rate of BacteriophagesInfluential work since 2022
- Pick up a classic book: The theory of ultrafiltersThe most-reprinted book on the subject
- Read the landmark paper: Ultrafilter Membranes and Ultrafiltration.Cited 333 times
- Go sideways: Ultrafilter on a setA closely related topic
- Go sideways: Boolean prime ideal theoremA closely related topic
📖 Definitions
Noun A device that performs ultrafiltration.
Noun A proper filter which has a law of dichotomy for complements.
Noun A filter (subset of a poset) that is maximal as a set with respect to the definition of proper filter.
Verb To filter by ultrafiltration.
🏆 Landmark papers (most cited)
Ultrafilter Membranes and Ultrafiltration.
Sequential reaction and product separation on molecular films of glucoamylase and glucose oxidase assembled on an ultrafilter
Optimization of a Reusable Hollow-Fiber Ultrafilter for Simultaneous Concentration of Enteric Bacteria, Protozoa, and Viruses from Water
Glomerular basement membrane as a compressible ultrafilter
The Power of the Ultrafilter Theorem
Triquotient maps via ultrafilter convergence
Evaluation and optimization of a reusable hollow fiber ultrafilter as a first step in concentrating cryptosporidium parvum oocysts from water
Hydrolysis of cellulose by cellulases of Sporotrichum cellulophilum in an ultrafilter membrane reactor
🆕 Influential since 2022
Choice of Ultrafilter Affects Recovery Rate of Bacteriophages
Collagen IV of basement membranes: II. Emergence of collagen IVα345 enabled the assembly of a compact GBM as an ultrafilter in mammalian kidneys
A model-based performance analysis of integrated chromatography-ultrafilter separation systems for monoclonal antibody (mAb) manufacturing
Mechanistic study of fouling hybrid PES-ionic liquid ultrafilter membrane during oily wastewater treatment; effect of surfactant type, salinity, and pH
Monochromatic exponential triples: An ultrafilter proof
📚 Books worth reading
The theory of ultrafiltersW. W. Comfort, S. Negrepontis · 1974- 📕Combinatorics of numbersI. Protasov · 1997
- 📕Ultrafilters Throughout MathematicsIsaac Goldbring · 2022
Ultrafilters and topologies on groupsYevhen G. Zelenyuk · 2011- 📕Structural properties of idealsJ. E. Baumgartner · 1982
- 📕Étude combinatoire et topologique des filtres sur NMaryvonne Daguenet · 1977
- 📕Filters and ultrafilters over definable subsets of admissible ordinalsJ. C. M. Baeten · 1986
- 📕Ultrafilters across mathematicsUltramath 2008: Applications of Ultrafilters and Ultraproducts in Mathematics (2008 Pisa, Italy) · 2010
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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